Find the angle between the vectors u= −3,1
and v= 2,4

Question

Find the angle between the vectors u= −3,1
 and v= 2,4

anonymous · Answer

Take dot product between two vector

anonymous · Answer

$$\alpha = \cos^{-1} \frac{ (-3 \times 2 ) + (1 \times 4 ) } { \sqrt{(-3)^2 +1^2 } \times \sqrt{2^2 +4^2} }  $$

anonymous · Answer

hm
if i get arccos 10/root(200)   how do i change $$\sqrt{200}$$ to something easier?

anonymous · Answer

dot product ftw

anonymous · Answer

You can also use a ruler to check your answer

anonymous · Answer

a protractor ruler

myininaya · Answer

$$\sqrt{200}=\sqrt{100*2}=10\sqrt{2}$$

myininaya · Answer

$$\alpha=\cos^{-1}\frac{-2}{10*\sqrt{2}}=\cos^{-1}\frac{-2*\sqrt{2}}{10*\sqrt{2}*\sqrt{2}}=\cos^{-1}\frac{-2\sqrt{2}}{20}=\cos^{-1}(\frac{-\sqrt{2}}{10})$$

anonymous · Answer

You can actually find the angle of both using trigonometry then find the difference between both angles....if you didn't know that dot product formula